Investing.com - Shares in Tokyo gained despite a downward revision in wages data with Hong Kong and Shanghai also up and Sydney down.
The Nikkei 225 rose 0.66%, while the Shanghai Composite jumped 2.72% and the Hang Seng index gained 0.40%.
Offsetting the trend, the S&P/ASX 200 fell 0.24%.
The strong Australian dollar and federal spending plans are the key variables in assessing the case for a further rate cut from a record low 2%, the Reserve Bank of Australia said in the minutes of its May meeting that were released on Tuesday.
Since the May meeting, Australia released a federal budget that leaned more toward spending control than stimulus.
In Japan, March total wages were revised down to unchanged from a preliminary gain of 0.1%.
Overnight, U.S. stocks were higher after the close on Monday, as gains in the Healthcare, Financials and Telecoms sectors led shares higher.
At the close in New York, the Dow Jones Industrial Average rose 0.14% to hit a new all time high, while the S&P 500 index climbed 0.30%, and the NASDAQ Composite index added 0.60%.
Overnight, investors turned their attention to the Federal Reserve's upcoming policy meeting.
Markets are also braced amid fresh concerns over the prospects of a Greek default.
Athens is scrambling to reach a cash-for-reform deal with its international lenders in time to avoid a cash crunch.
Over the weekend, a leaked memo from the International Monetary Fund showed that there is "no possibility" that Athens can meet a loan repayment due on June 5 without a deal to unlock outstanding bailout funds.
Last week Greece came close to defaulting on a €750 million IMF repayment, which it ultimately made by tapping emergency reserves in its holding account at the IMF.